We are pleased to announce that the next ITMP seminar will be held on Wednesday, Dec 9, at 18:00 (Moscow time). The seminar will be arranged via Zoom.
Speaker: Fedor Popov, Princeton University
Title: RG Limit Cycles and "Spooky" Fixed Points in Perturbative QFT
Abstract: We study quantum field theories with sextic interactions in
3−ϵ dimensions, where the scalar fields ϕab form irreducible representations under the O(N)2 or O(N) global symmetry group. We calculate the beta functions up to four-loop order and find the Renormalization Group fixed points. In an example of large N equivalence, the parent O(N)2 theory and its anti-symmetric projection exhibit identical large N beta functions which possess real fixed points. However, for projection to the symmetric traceless representation of O(N), the large N equivalence is violated by the appearance of an additional double-trace operator not inherited from the parent theory. Among the large N fixed points of this daughter theory we find complex CFTs. The symmetric traceless O(N) model also exhibits very interesting phenomena when it is analytically continued to small non-integer values of N. Here we find unconventional fixed points, which we call "spooky." They are located at real values of the coupling constants gi, but two eigenvalues of the Jacobian matrix ∂βi/∂gj are complex. When these complex conjugate eigenvalues cross the imaginary axis, a Hopf bifurcation occurs, giving rise to RG limit cycles. This crossing occurs for Ncrit≈4.475, and for a small range of N above this value we find RG flows which lead to limit cycles.
If you want to join the seminar please register here before 15:00, December 9.
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